The Elevator Problem - PowerPoint PPT Presentation

The Elevator Problem. Christine Belledin The North Carolina School of Science and Mathematics Teaching Contemporary Mathematics Conference 2014. What is mathematical modeling?. According to the Common Core Standards for High School: Modeling is the process of choosing and using appropriate

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“Never before, in all my math experiences, had I seen a problem as open ended and varying as this one. Working on a problem like this with no obvious answer and many different options was a wholly new experience for me. This problem helped me visualize the role math could and most likely will play in my future.”

In some buildings, all of the elevators can travel to all of the floors, while in others, the elevators are restricted to stopping only on certain floors. Why? What might be the advantage of having elevators that travel only between certain floors?

Suppose a building has 5 floors (1-5) that are occupied. The ground floor (0) is not used for business. Each floor has 60 people working on it. There are three elevators (A, B and C) available to take these employees to their offices in the morning. Everyone arrives at approximately the same time and enters the elevators on the ground floor. Each elevator holds 10 people and takes approximately 25 seconds to fill on the ground floor. The elevators then take 5 seconds between floors and 15 seconds on each floor on which it stops.

If all elevators go to all floors, how long will it take everyone to get to work?

If 80 people were late using the unrestricted elevators, approximately what time did the employees begin arriving at the ground floor?

Reassign the elevators to transport the employees to their offices as quickly as possible. What arrangement produces the shortest time? If this arrangement had been used today, would everyone have arrived at their floor on time?

“It was also a very complex problem, much more complex than I had ever done before. We had to set assumptions to reduce the amount of variables and make the project manageable. Even with the assumptions the problem was daunting. We had to break it down logically instead of just trying to plug it into a memorized equation. This thought process is very common in this class, and while I found it confusing and hard, I end with deeper understanding of how to do the problems.”

“The elevator problem was probably the first time in the class that I felt like I was trying to comprehend something completely beyond my intelligence, but eventually I figured out what we are doing.”

“I absolutely loved the elevator problem because it was so intricate and complex. I also liked that it might actually be helpful one day and have real world application. I liked that in order to find the one of many possible final solutions, you must first solve for one tiny section, how long it takes to get to one floor, and then apply it to the whole process. I think this was also one of my favorite problems because it was a reasoning problem instead of a computation problem. I wish we would do more problems like these more often.”

“I don't know what a profession that focuses on efficiency (workplace or public) is called, but I would love to work out things like this for a living.”

“In most of my other math classes, the concepts were mostly superficial; in the sense that we only learned the basics and processes of a certain idea without working on how it could be used in real life. Of course, this was often nice and easy, bit if I'm looking to work in a STEM field one day, it is crucial to understand the applications of the different things we learn.”

President’s Council of Advisors on Science and Technology, PCAST, Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics, Office of Science and Technology Policy, Washington DC, February 2012, http://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-engage-to-excel-final_2-25-12.pd